We have developed a simulation technique, based on a dynamic mean field theory to describe the evolution of a melt of liquid crystalline polymers that is quenched below its isotropic-nematic transition temperature. The polymers are described by chains characterized by a bending energy depending on the angles between consecutive chain segments and a Maier Saupe term accounting for the effect of mutual alignment of the segments in the melt. The equations for the time evolution of the system depend on coarsened variables, which are the density rho(r) and the orientation distribution (S) under bar (r). The density field rho evolves according to a diffusion-type equation, whereas the orientation field (S) under bar follows a growth equation.